S-HARP : A Parallel Dynamic Spectral

Computational science problems with adaptive meshes involve dynamic load balancing when implemented on parallel machines. This dynamic load balancing requires fast partitioning of computational meshes at run time. We present in this report a fast parallel dynamic partitioner, called SHARP. The underlying principles of S-HARP are the fast feature of inertial partitioning and the quality feature of spectral partitioning. SHARP partitions a graph from scratch, requiring no partition information from previous iterations. Two types of parallelism have been exploited in SHARP, fine-grain loop-level parallelism and coarse-grain recursive parallelism. The parallel partitioner has been implemented in Message Passing Interface on Cray T3E and IBM SP2 for portability. Experimental results indicate that SHARP can partition a mesh of over 100,000 vertices into 256 partitions in 0.2 seconds on a 64-processor Cray T3E. SHARP is much more scalable than other dynamic partitioners, giving over 15-fold speedup on 64 processors while ParaMeTiS1.0 gives a few-fold speedup. Experimental results demonstrate that SHARP is three to 10 times faster than the dynamic partitioners ParaMeTiS and Jostle on six computational meshes of size over 100,000 vertices. 1. Andrew Sohn, Dept. of Computer Science, New Jersey Institute of Technology, Newark, NJ 07102-1982; sohn@cis.njit.edu. 2. Horst Simon, NERSC, MS 50B-4230, Lawrence Berkeley National Laboratory, Berkeley, CA 94720; simon@nersc.gov. This work was supported by the Director, Office of Energy Research, Office of Computational and Technology Research, of the U.S. Department of Energy, under Contract No. DE-AC0376SF00098.